Chapter 8.4, Problem 50E

Find the sequence with each of these functions as its exponential generating function.

a) $f\left(x\right)=e^{3x}$

b) $f\left(x\right)=2e^{-3x+1}$

c) $f\left(x\right)=e^{4x}+e^{-4x}$

d) $f\left(x\right)=\left(1+2x\right)+e^{3x}$

e) $f\left(x\right)=e^x-\left(1/\left(1+x\right)\right)$

f) $f\left(x\right)=x{e}^x$

g) $f\left(x\right)=e^{x3}$